WASHINGTON — The Supreme Court appears likely to rule for an inmate on Texas’ death row who was denied money to investigate his history of mental illness and other claims that could spare him from being executed.

The case the justices heard Monday involves Carlos Manuel Ayestas, an immigrant from Honduras who was sentenced to death for strangling a woman in Houston.

The immigrant’s lawyers for his appeals in the federal court system argued that his trial and state appellate lawyers did not do enough to look into the man’s past in search of mitigating evidence that might persuade a jury not to impose a death sentence.

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But federal courts refused a request for money to investigate, despite a federal law aimed at improving legal representation in capital punishment cases.

The federal Capital Justice Act allows lawyers for indigent defendants facing the death penalty to apply for money for investigative, expert, or other services that are reasonably necessary to assemble the kind of mitigating evidence that might persuade the jury to forgo a recommendation of death.

In separate action Monday, the Supreme Court turned away an appeal from a Louisiana dirt farmer who complained that a local flood control district took his soil without paying enough for it.